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A208190 Number of distinct 5-colored necklaces with n beads per color. 2

%I

%S 1,24,11352,11211216,15277017432,24934429725024,45695805591924048,

%T 90784545100668913392,191417861328837588057432,

%U 422458626725600682518100816,966695515158024410709527456352,2277925055026596846727033776223440,5499697195473757755182168765034005328

%N Number of distinct 5-colored necklaces with n beads per color.

%H Alois P. Heinz, <a href="/A208190/b208190.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = Sum_{d|n} phi(n/d)*(5*d)!/(d!^5*5*n) if n>0 and a(0) = 1.

%F a(n) ~ 5^(5*n-1/2) / (4 * Pi^2 * n^3). - _Vaclav Kotesovec_, Aug 23 2015

%e a(0) = 1: the empty necklace.

%e a(1) = 24: {01234, 01243, ..., 04321}.

%p with(numtheory):

%p a:= n-> `if`(n=0, 1, add(phi(n/d) * (5*d)!/(d!^5 *5*n), d=divisors(n))):

%p seq(a(n), n=0..14);

%Y Column k=5 of A208183.

%Y Cf. A000010, A000142.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 24 2012

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)